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We present a systematic search for Type IIB supergravity solutions whose spacetimes include AdS 5 and S 2 factors, which would be candidate duals to N=2 four-dimensional Superconformal field theories. The candidate solutions encode the SU(2) R-symmetry geometrically on the S 2 and an additional Killing vector generates the U(1) R-symmetry. By analysing the Killing spinor equations we show that no such solutions exist. This suggests that if Type IIB backgrounds dual to N=2 SCFTs exist, the SU(2) R-symmetry is realised non-geometrically. Finally, we also show that, in the context of both N=1 and N=2 Type IIB backgrounds with an AdS 5 factor, the only candidate U(1) R-symmetry Killing vector directions are the ones that appear for generic values of the Killing spinors; no further Killing vectors exist for special values of the Killing spinors.
|Uncontrolled Keywords:||AdS-CFT Correspondence; Supergravity Models|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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